172. Color glass condensate and glasma
Save This Post as PDFI am currently reading a paper that, I should admit, I absolutely fell in love with – the one by Larry McLerran called “A brief introduction to the color glass condensate“. What is the reason for me to show up warm feelings? This is because the concentration of non-trivial physical ideas per page is so enormously high in the paper, because the emphasis is on physics and physical ideas rather than on formalities or model building, and because Larry typically just shows you the tail of the idea hiding its body in references – this keeps my mind always focused (clearly, I don’t want to go through tones of references to understand what physics is about 
)
1. Dynamics of heavy ion collisions
Imagine two heavy Au ions colliding with each other at ultrarelativistic velocities (that is what people do in Brookhaven all the time – collide Au ions). Both ions contain a very large number of neutrons and protons – in a sense, they can be visualized as large bulbs filled with gas of neutrons and protons (the characteristic size of an ion is much much larger than the proton size), and interaction between the ions is essentially reduced to the interaction between protons and neutrons they consist of.
Since the kinetic energy of the ion is larger than 
, the deconfinement is to happen in the process of collision, and we are supposed to see the state called quark-gluon plasma (quarks are consituents of protons and neutrons, while gluons mediate strong interaction between quarks). Approximately after 10 fm/c (1 fm is the characterisitic size of small hadrons) the quark-gluon plasma is hadronized and we are again left with ultrarelativistic protons and neutrons. But what exactly happens between the moment of collision and the hadronization time? Can we say something more about the state of matter at these times? QG plasma is weakly coupled, since the energies are high – so we should be able to quanitatively treat the matter degrees of freedom by means of perturbation theory.
Real life, as it turns out, is not so simple. The main difficulty is that although the plasma is weakly coupled, occupation numbers of gluons are very high (in fact, non-perturbatively high as 
), so naive Boltzmann approximation for kinetic equation describing dynamics od these ossupation numbers is not applicable. Yet, we are able to say many things about evolution of fields at time scales shorter than 10 fm/c.
As it turns out, at 
fm/c the matter can be described as so called color glass condensate, while at later time scales 
fm/c it can be described as glasma The latter state is transformed into proper quark-gluon plasma only at 
fm/c. So,…
2. What is color glass condensate?
As we said, immediately after the collision, the number of gluons is non-perturbatively high (it is surely much higher than quark occupation numbers – the latter are fermions, so their occupation numbers are no higher than 1), and we can effectively forget about quarks all together and focus only on the dynamics of gluons.
Gluon occupation numbers become large due to non-perturbative particle production in the process of collision (fields become really strong in the process) – particles are especially effectively produced in the deep IR. However, occupation numbers cannot be too large, since the backreaction of produced gluons becomes important (interaction between gluons is repulsive and has the order of magnitude 
) and shuts the particle production down. In practice, there exists a characteristic momentum scale 
such that occupation numbers are not to grow at 
. After particle production stops, distribution of gluons starts to slowly evolve towards the UV. The characteristic time scale of the dynamics of the distribution is of course 
.
What happens at 
? Gluons may still be produced there, but they see the IR gluon field with as the classical one (but stochastic, of course). That is why one talks about color glass – slowly evolving condensate of IR quasi-classical gluons.
3. What is glasma?
At later times, gluon distributions start to thermalize. As long as occupation numbers in the IR remain non-perturbatively large, the quantum state describing the gluons after collision remains coherent – phases of different IR gluon modes remain correlated. Some deep IR part of the distribution remains in this coherent state till the hadronization time. That is why the state of matter during this period is called Glasma – it is neither color glass condensate anymore (the correlation of phases started to break down already in the IR, and UV part of the distribution is a pure gluon plasma), nor the quark-gluon plasma (there is still noticeable coherence pattern in the IR).
4. What’s not so clear to me yet
Experimental data indicate that QG plasma is thermalized at very early times (definitely earlier than 10 fm/c, the hadronization time scale). How and why this happens if there is still strong coherence pattern in the IR? Most probably, early thermalization automatically means that randomization of phases and breakdown of coherence pattern in the IR happens really early (I would say – as early as 1 fm/c after the collision). RHIC experts, who read this blog, could you kindly comment on this? Does glasma really have a time window to exist?
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Hi Dmitry! Did all occurrences of “fm/s” went to be meant “fm/c” where “c” is the speed of light? If not, what is fm/s as a unit of time?
Unfortunately, I didn’t quite understand what a color glass condensate (and glasma) is, even though you made a good job in saying where it is (the context) and what it is not.
Would you mind inserting a real definition into your text? Thanks a bucket.
Dear Lubos,
Yes, everything was in units fm/c. Thanks a lot!
Dmitry.
Dmitry,
Is it possible that some sort of absorbing phase transition (APT)occurs at very short times in glasma? This phase transition may be able to sustain coherence of gluon plasma and prevent thermalization beyond the hadronization time scale. It is known that APT drives components in reaction-diffusion processes to fall into absorbing states where thermal fluctuations are strongly suppresed. Your thoughts?
Regards,
Ervin
Hi Ervin
I think, you want to say that intermediate time behavior of gluon distribution functions is described by dynamical RG fixed point. I have no idea – maybe yes, maybe no, anyway, already at 10 fm/c hadronization happens and almost all information about this early stage is lost.
My impression is that QGP is not thermalized completely (at least not at short time scales I am talking about), instead, instead, what is called prethermalization happens:
fm/c, Boltzmann exponential tail is definitely not what is seen. On the other hand, gluon distribution function can be approximately described by Rayleigh-Jeans, so a kind of effective temperature is present in the system – this is what I meant by prethermalization. The nice thing is that prethermalization
gluon occupation numbers are still extremely high at
(contrary to full thermalization) does not automatically imply that coherence pattern in the IR breaks down.
Cheers,
Dmitry.
Hi Dmitry,
But if information is lost at 10 fm/c already, how can one prove that prethermalization actually takes place and phase coherence of QGP is still unbroken? Is there experimental evidence for the Rayleigh-Jeans distribution function or is it just a working hypothesis regarding what happens prior to hadronization?
Regards,
Ervin
Hi Ervin
I don’t think that anybody is able to measure gluon distribution function at these time scales, so yes, Rayleigh-Jeans is working hypothesis. What is observed in particular is the effective equation of state of the QGP, which reaches its equilibrium value at early times.
Cheers,
Dmitry.